Some rings for which the cosingular submodule of every module is a direct summand
| dc.contributor.author | Keskin, Derya Tütüncü | |
| dc.contributor.author | Orhan, Nil Ertas | |
| dc.contributor.author | F., Patrick Smıth | |
| dc.contributor.author | Trıbak, Rachid | |
| dc.date.accessioned | 2024-09-29T16:35:03Z | |
| dc.date.available | 2024-09-29T16:35:03Z | |
| dc.date.issued | 2014 | |
| dc.department | Karabük Üniversitesi | en_US |
| dc.description.abstract | The submodule Z(M) = ∩{N | M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P ) if Z(M) is a direct summand of M for every R-module M . It is shown that a commutative perfect ring R has (P ) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M ∈ Mod−R | ZR(M) = 0} is closed under factor modules, then R has (P ) if and only if the ring R is von Neumann regular. | en_US |
| dc.identifier.endpage | 657 | en_US |
| dc.identifier.issn | 1300-0098 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.startpage | 649 | en_US |
| dc.identifier.trdizinid | 186864 | en_US |
| dc.identifier.uri | https://search.trdizin.gov.tr/tr/yayin/detay/186864 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14619/12462 | |
| dc.identifier.volume | 38 | en_US |
| dc.indekslendigikaynak | TR-Dizin | en_US |
| dc.language.iso | en | en_US |
| dc.relation.ispartof | Turkish Journal of Mathematics | en_US |
| dc.relation.publicationcategory | Makale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Matematik | en_US |
| dc.title | Some rings for which the cosingular submodule of every module is a direct summand | en_US |
| dc.type | Article | en_US |
